COMM121 (Statistics For Business) UNIVERSITY OF WOLLONGONG FACULTY OF BUSINESS Tutorial 2 Week 5 Chapter 4 4.5 For each of the following, indicate whether the type of probability involved is an example of a priori classical probability, empirical classical probability or subjective probability. a. The next toss of a fair coin will be heads. b. Italy will win soccer's World Cup the next time the competition is held. c. The sum of the faces of two dice will be 7. d. The train taking a commuter to work will be more than 10 minutes late. 4.6 For each of the following, state whether the events are mutually exclusive and/or collectively exhaustive. If they are not mutually exclusive and/or collectively exhaustive, either reword the categories to make them mutually exclusive and collectively exhaustive or explain why this would not be useful. a. An exit poll in an Australian federal election asked voters if they had voted for the Labor or the Coalition candidate. b. Respondents were classified by type of car they drive: Australian, American, European, Japanese or none. c. People were asked, 'Do you currently live in (i) an apartment or (ii) a house?' d. A product was classified as defective or not defective. 4.8 A researcher has completed a survey of 10,000 viewers in a regional city to determine which TV network they watch most weekdays during the 6 pm to 7 pm time slot. The results are: A surveyed viewer is chosen at random. Find the probability that during the 6 pm to 7 pm time slot the viewer: a. watches an ABC channel b. watches ABC or SBS c. watches neither ABC nor SBS d. watches one of the networks Seven, Nine or Ten e. does not watch one of the networks Seven, Nine or Ten 1 4.9 A sample of 500 consumers is selected in a large metropolitan area to study consumer behaviour. Among the questions asked was 'Do you enjoy shopping for clothing?' Of 240 males, 136 answered yes. Of 260 females, 224 answered yes. Construct a contingency table or a Venn diagram to evaluate the probabilities. What is the probability that a surveyed consumer chosen at random: a. enjoys shopping for clothing? b. is a female and enjoys shopping for clothing? c. is a female or enjoys shopping for clothing? d. is a male or a female? 4.15 The following table gives the labour force status of Australian civilian population aged 15 years and over in November 2013: a. What is the probability that a randomly selected person is female? b. What is the probability that a randomly selected male is not employed? c. Suppose you know that a person is employed full-time. What is the probability that they are female? d. Are the two events 'employed full-time' and 'female' statistically independent? Explain. e. What is the probability that a randomly selected person is a male in full-time employment? f. The unemployment rate is defined as the percentage of the labour force that is unemployed and either looking for work or not looking for work. What is the unemployment rate for males, females and overall? g. The participation rate is defined as the percentage of the civilian population in the labour force, either employed or unemployed. What is the participation rate for males, females and overall? 4.18 A sample of 500 consumers was selected in a large metropolitan area to study consumer behaviour with the following results: a. What is the probability that a randomly chosen female consumer does not enjoy shopping for clothing? b. Suppose the chosen consumer enjoys shopping for clothing. What is the probability that the individual is male? c. Are enjoying shopping for clothing and the gender of the individual statistically independent? Explain. 2 4.56 The employees of a company were surveyed and asked their educational background and marital status. Of the 600 employees, 400 had university degrees, 100 were single and 60 were single university graduates. a. Construct a contingency table for this problem. b. Find the probability that a randomly selected employee of the company is single or has a university degree. c. What percentage of single employees have university degrees? d. Are gender and educational background statistically independent? Explain. Chapter 5 5.3 Using the company records for the past 500 working days, the manager of Konig Motors has summarised the number of cars sold per day in the following table: a. Form the probability distribution for the number of cars sold per day. b. Calculate the mean or expected number of cars sold per day. c. Calculate the standard deviation. 3 5.19 Research has shown that only 60% of consumers read every word, including the fine print, of a service contract. Assume that the number of consumers who read every word of a contract can be modelled using the binomial distribution. A group of five consumers has just signed a 12-month contract with an ISP (Internet service provider). a. What is the probability that: i. all five will have read every word of their contract? ii. at least three will have read every word of their contract? iii. less than two will have read every word of their contract? b. What would your answers be in (a) if the probability is 0.80 that a consumer reads every word of a service contract? 5.23 When a customer places an order with Rudy's On-Line Office Supplies, a computerised accounting information system (AIS) automatically checks to see whether the customer has exceeded their credit limit. Past records indicate that the probability of customers exceeding their credit limit is 0.05. Suppose that, on a given day, 20 customers place orders. Assume that the number of customers that the AIS detects as having exceeded their credit limit is distributed as a binomial random variable. a. What are the mean and standard deviation of the number of customers exceeding their credit limits? b. What is the probability that no customer will exceed their limit? c. What is the probability that one customer will exceed their limit? d. What is the probability that two or more customers will exceed their limits? 4